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ArticleOriginal scientific text

Title

On the isoperimetry of graphs with many ends

Authors 1

Affiliations

  1. Laboratoire de Mathématiques E. Picard, UMR CNRS 5580, Université Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse Cedex, France

Abstract

Let X be a connected graph with uniformly bounded degree. We show that if there is a radius r such that, by removing from X any ball of radius r, we get at least three unbounded connected components, then X satisfies a strong isoperimetric inequality. In particular, the non-reduced l2-cohomology of X coincides with the reduced l2-cohomology of X and is of uncountable dimension. (Those facts are well known when X is the Cayley graph of a finitely generated group with infinitely many ends.)

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Colloquium Mathematicum
1998/78/2
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Pages:
307-318
Main language of publication
English
Received
1997-11-28
Accepted
1998-04-27
Published
1998
Exact and natural sciences